Modelling and Simulation of Multiple Single - Phase Induction Motors in Parallel Operation

Transcription

1 Poceedn of the 8th WSEAS Int. Confeence on Automatc Contol Modeln and Smulaton Paue Czech Republc Mach -4 6 (pp95-) Modelln and Smulaton of Multple Snle - Phae Inducton Moto n Paallel Opeaton SAKRAWEE RAWEEKU THAATCHAI KUWORAWAICHPOG and SARAWUT SUJITJOR School of Electcal Enneen Inttute of Enneen Suanaee Unvety of Technoloy Unvety Avenue Muan Dtct ahon Ratchama 3 THAIAD abtact:- The development of a tate-pace model epeentn multple nle-phae nducton moto n paallel connecton decbed n th pape. We peent the model n a eneal expeon baed on the dqfame pncple. The et of paallel moto aumed to be fed by a nle nvete ouce. Alo mulaton eult on fou dve condton ae dcued Key -wo: nle-phae nducton moto paallel connecton modelln. Intoducton Mot ndute n developn counte ae baed on acultue. Unle othe heavy ndute acultual ndute eque mall ze machne n poducton plant. In th fahon thee-phae nducton moto ae not utable becaue they ae uually ove-atn. Althouh any lae-ze theephae nducton moto can be opeated at a facton of the atn t not a ood eaon to do o due to neffcency and uneconomy. Inceanly many pocee and offce-ued applance ae detemned to employ mple and cheap nle-phae moto. In ome ndute uch a tach textle food pocen etc a hunded of nle-phae nducton moto ae ntalled to eve loa. In pactce ue of one nvete to upply one moto cotly and alo neffcent. To educe cot paallel connecton of multple nle-phae nducton moto fed by a nle nvete [][] an altenatve due to t mplcty and cheapne. Theefoe mpovement of effcent opeaton fo a paallel-connected multple nle-phae nducton moto dve [3] vtal to ve lo mnmzaton and mnmum opeatn cot. In th pape we attempt to develop a mathematcal model fo multple nle-phae nducton moto n paallel connecton a decbed n tate-pace fom. Th modelln baed on the two-ax dq fame theoy whch play an eental ole fo hh-effcent nducton moto dve technoloy. The analye appeaed n th pape cont of fou man pat that ae: ) nle-phae nducton moto model n tatonay efeence ) modelln of multple nle-phae nducton moto n paallel connecton ) mulaton eult conducted by fou loadn cenao and v) concluon. Snle-Phae Inducton Moto Model n Statonay Refeence A nle-phae nducton moto condeed to have tato and oto wndn. A hown n fue the tato wndn compoe of the man and the auxlay wndn [4]. To develop the moto model the moto telf can be condeed a a twophae o two-ax devce. In tem of two axe the d and the q axe ae pependcula. The development of the moto tate model utlze the dq-fame pncple and the efeence fame theoy [5]. The late theoy allow the tanfomaton of oto vaable to the tato de. F. Wndn compoton of a nle-phae nducton moto.

2 Poceedn of the 8th WSEAS Int. Confeence on Automatc Contol Modeln and Smulaton Paue Czech Republc Mach -4 6 (pp95-) The daam n f. [6] eveal the oentaton of the moto wndn. In the fue the ubcpt q denote any quantte belonn to the tato man wndn (the tato q-ax wndn) denote thoe belonn to the tato auxlay wndn (the tato d-ax wndn) q and d epeent the ame but fo the oto wndn n the q- and the d-axe epectvely. In the ame fue the chaacte I and denote voltae cuent and tun of the wndn epectvely. The follown ubecton peent the ummay of the moto tate model fo the tato and the oto epectvely. The Stato The voltae on the tato pat can be mply expeed by q = qq qq pq q p p qq = q pq p p q q q qd d p p d d n whch p denote d. The above expeon can F. Oentaton of the tato and the oto wndn. The q and q axe have the phae dffeence of θ. Baed on the wndn oentaton a decbed one can wte the equaton () n whch the upecpt and denote the tato and the oto de epectvely. q d coθ = nθ o n a compact fom of whee de and.e. θ nθ coθ q d () I x = I x () Ix denote any quantte tanfomed fom the oto de to the tato de I denote any quantte on the oto x [ ] denote the tanfomaton matx coθ nθ = nθ coθ. be eaaned n the matx fom a n (3). q q p = pq pq q p qq qd q p (3) q qq d qq The Roto Due to the oto ymmetcty the wndn tun on the d- and the q-axe ae equal. The etance ae alo equal.e. q = d =. The voltae on the oto pat can be mply expeed by q = qq q qq p p p q d qq q = dd dq pq pd dq pq o n the matx fom of q d q p = pdq qq q q d p p pqd q d pdd d qq q q p (4) dq d By tanfen all quantte to the tato efeent fame the tate-pace matx epeentn one nle-phae nducton moto can be ummazed a hown n equaton (5)

3 Poceedn of the 8th WSEAS Int. Confeence on Automatc Contol Modeln and Smulaton Paue Czech Republc Mach -4 6 (pp95-) whee = d A B v = (5) T q q d T v = q q d A D C = B = D q C = ωmqnθ ωmqco θ ωmqcoθ ωmqcoθ and D ωmqnθ ωmqcoθ ωq coθ ωmqco θ = coθ nθ lq mq mq mq ( ) ω nθ ω coθ lq q mq q coθ nθ ( ) mq l mq mq nθ coθ ( l mq ) mq q = man wndn tun = auxlay wndn tun and q = d = = oto wndn tun. = q q = mq l q = qp = ( ) P = mq q q = ( ) l = ( ) q q l = ( ) l = q q q q = q q = ( = ) q d d d = q d (ema: ndcate the tanfomed quantte to the efeence q-ax of the tato.) Futhemoe the co nductance can be eplaced by the manetc nductance un the follown elaton [4] qq = lq qp = l P qq = qqp qd = qdp q = qp d = dp = P dd = lq dp qq lq q Conden the oto moton t mechancal model expeed by [6] dω P P Bmω() t = Te() t T() t Jm J m Jm whee T e denote electomanetc toque.e. P Te = ( ) mqq ( q nθ d co θ ) mq( q coθ d nθ) dθ and = ω Th model can be ewtten n a tate-pace fom a dω Bm P J [ Te T ] d ω = m J (6) θ m θ Combnn the electcal and the mechancal tate model eult n the equaton (7) epeentn a nle-phae nducton moto. d 4x R4 4 x 4x 4x dω B = ω J x4 m θ dθ ℵ 4 4 x 4x 4x P Te T J x4 m n whch T = 4x q q d A D C R = = 4x4 B D ℵ = = 4x4 (7)

4 Poceedn of the 8th WSEAS Int. Confeence on Automatc Contol Modeln and Smulaton Paue Czech Republc Mach -4 6 (pp95-) 3. Modelln of Multple (n) Paallel Connected Moto To analyze electomechancal chaactetc of n paallel nle-phae moto a combnaton of an ndvdual model fo each moto nee to be defned n a nle and lae-pae matx to epeent the ente ytem. F. 3 depct a oup of n-paallel connected moto. The model fo the th moto can be expeed explctly a equaton (7) wth ubcpt. et [Λ ] and q q Λ = d ω θ and q q Θ = d T e T d [ R ] [ R ] [ R ] M [ ℵ ] [ ℵ ] [ ℵ ] M x x x x 4x4 4x4 4x4 4x4 Θ 4x4 4x4 4x4 4x4 4x4 4x4 4x4 4x4 Θ Λ 3 = 3 Λ [ Θ x x x x 4x4 4x4 4x4 3 ] 4x4 M M M M O M M M M M O M M [ ] [ R ] n n n x x x x ℵ Θ n n x x x x (8) [Θ ] be tate and nput vecto of the th moto epectvely. The collectve matx equaton epeentn the oup of n-paallel connected moto can be wtten a equaton (8). F. 3 Schematc daam fo a oup of n paallel moto. 4. Smulaton Reult To vefy effectvene coecton and accuacy of the developed model fou tet-cae cenao wee aned n whch thee moto dvn epaate centfual pump connected n paallel fom the tet bed. The fou tet cae ae detaled a follow [7]-[]. Cae : all tet moto ae techncally the ame n both moto paamete and moto loa. Moto : Paamete et oad Moto : Paamete et oad Moto 3: Paamete et oad Cae : paamete of each moto ae equal but they hae a dffeent poton of load. Moto : Paamete et oad Moto : Paamete et oad Moto 3: Paamete et oad 3 Cae 3: load of each tet moto equal whle the paamete ae dffeent. Moto : Paamete et oad Moto : Paamete et oad Moto 3: Paamete et 3 oad Cae 4: nethe paamete no load of the moto ae equal. Moto : Paamete et oad Moto : Paamete et oad Moto 3: Paamete et 3 oad 3 and load ae lted below oad toque :.8-4 ω.m oad toque : ω.m oad toque 3: ω.m Table Moto paamete []-[3]. Paamete et pole q ( Ω ) ( Ω ) ( Ω ) mq (H) l (H) lq(h) l J (.m ) B m ( m/ad/ec) (H)

5 Poceedn of the 8th WSEAS Int. Confeence on Automatc Contol Modeln and Smulaton Paue Czech Republc Mach -4 6 (pp95-) Table Steady-tate pefomance of each tet cae Cae Cae Cae 3 Cae 4 M M M3 M M M3 M M M3 M M M3 Supply Cuent (A m ) Moto Cuent (A m ) Moto Speed (pm) oad Toque (.m) Moto Slp The mulaton fo each tet cae wa conducted by applyn a - 5-Hz nuodal voltae ouce to eneze the moto oup. To befly peent the tet eult teadytate value of ome ey chaactetc fo each moto and fo the ente oup ummazed n table. In addton elevant epone n tme doman of the fouth cae ae elected and hown n f.4-9. Iq I 5 5 Moto Speed (pm) at nput oltae = Moto Speed (pm) at nput oltae = Moto 3 5 Speed (pm) at nput oltae = tme() F. 6 Moto pee (pm) of cae Iq Iq I I cuent Moto cuent Moto cuent Moto tme() tme() F. 4 Stato cuent (A) of cae tme() F. 7 Cuent (A) dawn by each moto of cae 4 5 um of cuent (A) Iq Id Iq Iq Id Id tme() F. 8 Cuent (A) of the moto oup of cae 4 5 Moto Moto tme() tme() F. 5 Roto cuent (A) of cae Moto tme() F. 9 Moto toque (.m) of cae 4

6 Poceedn of the 8th WSEAS Int. Confeence on Automatc Contol Modeln and Smulaton Paue Czech Republc Mach -4 6 (pp95-) A can be een the mulaton eult fom the fou tet cae eveal electomechancal chaactetc fo all moto of the oup. By the method popoed n th pape eveal moto connected n paallel can be analyzed numecally. Th model mple but effcent to be ncluded nto a mulaton alothm of a hh-pefomance dve patculaly n a paallel opeaton of multple nle-phae nducton moto. In ode to educe model complexty ome can beneft nfcantly fom th model. 5. Concluon The development of the tate model fo multple nle-phae nducton moto n paallel connecton ha been explaned wth mulaton eult peented. The model n eneal fom ueful fo pactcal condeaton unde vaou load and dve condton. Ou futhe eeach to develop enole dve technoloy on the ba of the eult peented heen. Alo pefomance lmt and tablty wll be thoouhly nvetated. A mathematcal model n th pape dect and mple. Althouh the ytem matx eultn fom th model zable t emaably pae. Wth the help fom MATAB latet veon oluton of the tme ee tate equaton epeentn the moto oup ae ealy obtaned. Refeence: [] Y.Matumoto S.Oza and A.Kawamua A novel vecto contol of nle-nvete multple-nducton-moto dve fo Shnanen tacton ytemieee Appled Powe Electonc Confeence and Expoton ( APEC.) ol. pp [] B.Wu S.B. Dewan and P.C.Sen A Mod- -fed Cuent ouce nvete fo a multple nducton moto dve ytem IEEE Tan. On Powe Electonc ol.3 o. 988 pp. 6. [3] M.B.R.Coea C.B.Jacobna A.M..ma ande.r.c. da Slva Snle-phae nducton moto dve ytem IEEE Appled Powe Electonc Confeence and Expoton ol. 999 pp [4] Chee-Mun on Dynamc Smulaton of Electc machney un MATAB /SIMUIKPentce Hall998 [5] R.Khnan Electc Moto Dve Modeln Analy and Contol Pentce Hall. [6] P.C. Kaue O.Waynczu and S.D. Sudhoff Analy of Electcal Machney Pcataway j ;IEEE Pe 995. [7] M.B.R.Coea C.B. Jacobna A.M.. ma and E.R.C. da Slva ecto contol tatee fo nle-phae nducton moto dve ytem IEEE Tan. on Induty Applcaton ol. 5o5 4pp [8] D.H.Jan oltae fequency and phaedffeence anle contol of PWM nvetefed two-phae nducton moto IEEE Tan. on Powe Electonc ol. 9 o pp [9] K.MatueY.KounoH.Kawaand S.Yoo- -mzo A peed-enole vecto contol method of paallel-connected dual nducton moto fed by a nle nvete IEEE Tan. on Induty Applcaton ol.38 o.6 pp [] K.Matue Y.Kouno H.Kawa and J. Oawa Chaactetc of peed enole vecto contolled dual nducton moto dve connected n paallel fed by a nle nvete IEEE Tan. on Induty Applcaton ol. 4 o. 4 pp [] C.Mademl I.Koed and T.Theodould Optmzaton of nlephae nducton moto-pat I: maxmum eney effcency contol IEEE Tan. on Eney Conveon ol. o. 5 pp [] K.Matue S.Tanuch T.Yohzum and K.am A peed-enole vecto contol of nducton moto opeatn at hh effcency tan coe lo nto account IEEE Tan. on Induty Applcaton ol.37 o. pp [3] M.B.R.Coea C.B. Jacobna A.M.. ma and E.R.C. da Slva Roto-fluxoented contol of a nle-phae nducton moto dveieee Tan. on Powe Electonc ol. 47 o.4 pp